Question

Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Answer 1

the Greatest Integer Function is also known as Floor Function
 he floor function, denoted bxc is a function R → Z. Its value is the largest integer that is less than or equal to x.
so it has two values so for sure it has not one - one function
and since the image can have two values but not he pre-image so it is not onto function